Beginning Algebra, 11th Edition

3.3 The Slope of a Line

The slope of the line through and is

Horizontal lines have slope 0.

Vertical lines have undefined slope.

To find the slope of a line from its equation, solve
fory. The slope is the coefficient of x.

Parallel lines have the same slope.

The slopes of perpendicular lines are negative reciprocals
(that is, their product is - 1 ).

m 1 wherex 1 Zx 22.

change in y

change in x



y 2 y 1

x 2 x 1

1 x 1 ,y 12 1 x 2 ,y 22 The line through and has slope as follows.

The line has slope 0.

The line has undefined slope.

Find the slope of

Add

Divide by.

Slope

The lines and are parallel because both

have slope 3.

The lines and are perpendicular

because their slopes are - 3 and 31 ,and - (^3) A 31 B=- 1.
y=- 3 x- 1 y= 31 x+ 4
y= 3 x- 1 y= 3 x+ 4
y= - 4

3

4

x- 3

• 4 y=- 3 x+ 12 - 3 x.

3 x- 4 y=12.

x= 4

y=- 2

m=

- 5 - 3

4 - 1 - 22

=

- 8

6

= -

4

3

1 - 2, 3 2 1 4,- 52

CONCEPTS EXAMPLES

240 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

3.4 Writing and Graphing Equations

of Lines

Slope-Intercept Form

mis the slope.
1 0,b 2 is the y-intercept.

ymxb

Write an equation of the line with slope 2 andy-intercept

y= 2 x- 5

1 0,- 52.

(continued)

Point-Slope Form

mis the slope.
is a point on the line.

Standard Form

A,B, and Care real numbers and AandBare not both 0.

AxByC

1 x 1 ,y 12

yy 1 m 1 xx 12

Write an equation of the line with slope through

Substitute.

Definition of subtraction

Distributive property

Add 5.

The equation is written in standard form as

with and A=1,B=2, C=6.

x+ 2 y=6,

y=-^12 x+ 3

y=-

1

2

x+ 3

y- 5 =-

1

2

x- 2

y- 5 =-

1

2

1 x+ 42

y- 5 = -

1

2

3 x- 1 - 424

-^121 - 4 , 52.

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